Which should I pick among the four Brave Heroes?

All of them are great picks, but Brave Veronica could be the best one, because you can literally put her in any team and she'll be extremely useful and she's also used in many of f2p guides for more "advanced" in-game content. She combines healing, cavalry movement, buffing, debuffing and good offensive potential in a single character.

Pick Lyn and Veronica.
you wont regret it!
they are both ranged cavalry, with very powerful statline and skillset.

It's either Veronica or Hector.

Both are the best at what they do.
Veronica is the best healer in the game, and is useful on any team.
Hector is amazing as a frontline unit, being both tanky and strong. He's great out of the box, but has potential with niche builds.

The other two are very strong, but I think they're not the best options for new players to try out. So avoid those two on the free summon.

Celica - Interesting kit and hits hard as a truck, but with a free, tanky L!Ike that you'll get later on, she gets kinda outclassed. Not to mention, the red pool is inflated with other good sword units. So there is opportunity to get a sword unit that is better or performs the same.

Ephraim - Is interesting, but he relies somewhat on investment. He has no Distant counter, and while yes, he's a tanky boi, he kinda relies on his team to either give buffs for his weapon perk. Good nonetheless, and once you're able to support his needs, he's really great.

Hector - Probably hector's best form (imo). Hits hard consistently and tanky as always. Though, using armors early on when you just started can be kinda hard due to their mobility. However, he's still strong as always, just falls behind if not carried to spaces. He will probably be your best blue for a while until you are able to build someone else. Sure there is the free Fjorm to think about, but eh.

Veronica - To be honest, she does something a bit more than the rest. While yes, she performs her role greatly, has practically everything you need inside her kit asides a A slot skill, and has probably one the better weapon effects in the game... She's also probably going to be your best and only colorless unit in the game for quite a while. Let's be honest, the colorless pool is still... lacking, not counting the occasional seasonal or legendary. Asides like, a Sothe or Brave Lyn, summoning on the colorless pool is not really optimal. That being said, you are more than likely to get pitybroken by any of the other brave units than you would with Veronica... probably. It's RNG, afterall.

***TL;DR - Veronica will probably be your best colorless unit and healer for the majority of your early playtime. Hits hard, fast and safely. Honestly plays Brave Lyn with non-counterable playstyle, but better? Doesn't score well for arena though (as of now)... so if you care for bragging rights with crowns... then meh.

My pick list would be
Veronica
Hector
Epharim
Celica